In mass democracies, voting—in elections or referendums—is the main way in which most citizens can publicly express their political preferences. And yet this means of expression is sometimes perceived by them as highly frustrating, partly because it does not allow for much expression. Dominant voting methods lead to a reduction of options, pressure citizens to vote tactically at the cost of expressing their genuine preferences, and fail to convey what they really think about different candidates, parties, or (...) options. Yet citizens do not merely have a right to vote; they have a more fundamental right to political expression from which one can derive a right to a voting method that offers the most opportunities for expression among those satisfying other important requirements. The aim of this article is therefore to add this consideration about the importance of political expression to debates about voting methods that have mainly been conducted from the perspective of social choice theory. To illustrate what is at stake, it introduces evaluative voting methods (allowing voters to grade all of the candidates, parties, or options) as a promising way of honoring the right to political expression without jeopardizing other important properties of voting methods. (shrink)

The ideal of publicity plays an important role in contemporary legal and political philosophy. Yet, to date, it has not been brought to bear on the question of voting method choice. This paper aims to fix this. I argue that voting method publicity is a well-motivated requirement which reveals tradeoffs inherent to democracy between procedural and epistemic equality. I further explore the implications of voting method publicity to the normative status of plurality voting and its possible (...) alternatives. (shrink)

We propose a Condorcet-consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying the anti-vote-splitting criterion of independence of clones. In this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, in contrast to other clone-independent methods, Split (...) Cycle mitigates both “spoiler effects” and “strong no show paradoxes.”. (shrink)

In voting theory, monotonicity is the axiom that an improvement in the ranking of a candidate by voters cannot cause a candidate who would otherwise win to lose. The participation axiom states that the sincere report of a voter’s preferences cannot cause an outcome that the voter regards as less attractive than the one that would result from the voter’s non-participation. This article identifies three binary distinctions in the types of circumstances in which failures of monotonicity or participation can (...) occur. Two of the three distinctions apply to monotonicity, while one of those and the third apply to participation. The distinction that is unique to monotonicity is whether the voters whose changed rankings demonstrate non-monotonicity are better off or worse off. The distinction that is unique to participation is whether the marginally participating voter causes his first choice to lose or his last choice to win. The overlapping distinction is whether the profile of voters’ rankings has a Condorcet winner or a cycle at the top. This article traces the occurrence of all of the resulting combination of characteristics in the voting methods that can exhibit failures of monotonicity. (shrink)

Much of the theoretical work on strategic voting makes strong assumptions about what voters know about the voting situation. A strategizing voter is typically assumed to know how other voters will vote and to know the rules of the voting method. A growing body of literature explores strategic voting when there is uncertainty about how others will vote. In this paper, we study strategic voting when there is uncertainty about the voting method. We introduce (...) three notions of manipulability for a set of voting methods: sure, safe, and expected manipulability. With the help of a computer program, we identify voting scenarios in which uncertainty about the voting method may reduce or even eliminate a voter's incentive to misrepresent her preferences. Thus, it may be in the interest of an election designer who wishes to reduce strategic voting to leave voters uncertain about which of several reasonable voting methods will be used to determine the winners of an election. (shrink)

We consider scenarios with distributed decision processes, e.g., coupled majorities and personal union in parliament chambers, supranational decisions and supervisory boards. When computing the adoption rate for reaching a decision in these scenarios, multiple linear inequality restrictions in combinatorial countings are present. These rates cannot be computed in closed form. We introduce a general method for incorporating multiple inequality conditions in multiple majority decisions, which significantly reduces the number of involved summations and removes restrictions on the summation indices. Exact solutions (...) are provided through integral representations which can be evaluated numerically, and unrestricted, contracted sums over discrete events. Further, we provide methods to reduce the number of necessary summations by splitting or recurring the original problem to easier sub-problems. For five dedicated scenarios, full results are given which indeed require a single unrestricted summation only. (shrink)

The paper applies to approval voting, under which the voter casts a ballot by casting one vote for each of k candidates, wherek=;1,2, ? , m-1 and there are m candidates. I assume (following Brams and Fishburn) that each of the voter's 2=;-2 strategies is equally likely to be chosen. Election-outcome types include: the m-way tie;(m-1) -way ties with the runner-up trailing by 1,2,?,m votes; (m-2)-way ties, and so on. The frequency distribution of outcome types varies only with m (...) and n and is necessary to the calculation of the expected utilities of successive ballots cast, in the same election, by a voter under a variant of approval voting. This variant allows the voter to cast several complete ballots provided that he pays the respective prices, which could reasonably be based on the expected utilities. The paper describes a shortcut method of calculating the distribution of outcome types when m=;4 andn rises to levels that make straightforward calculation computationally infeasible. The shortcut involves the combining of an outcome type, instead of each member of that type, with each of the 14 strategies available to the incremental voter. In going fromn-1 to n, for n=3, the number of outcome types increases by a factor of (n+3)/n whereas, the number of combinations of strategies increases by a factor of 14. (shrink)

There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we report on the development of a framework for formalizing voting theory in the Lean theorem prover, which we have applied to verify properties of a recently studied voting method. While previous applications of interactive theorem proving to social choice have (...) focused on the verification of impossibility theorems, we aim to cover a variety of results ranging from impossibility theorems to the verification of properties of specific voting methods. In order to formalize voting theoretic axioms concerning adding or removing candidates and voters, we work in a variable-election setting whose formalization makes use of dependent types in Lean. (shrink)

Mathematical theory of voting and social choice has attracted much attention. In the general setting one can view social choice as a method of aggregating individual, often conflicting preferences and making a choice that is the best compromise. How preferences are expressed and what is the “best compromise” varies and heavily depends on a particular situation. The method we propose in this paper depends on expressing individual preferences of voters and specifying properties of the resulting ranking by means of (...) first-order formulas. Then, as a technical tool, we use methods of second-order quantifier elimination to analyze and compute results of voting. We show how to specify voting, how to compute resulting rankings and how to verify voting protocols. (shrink)

Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multi-issue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on (...) smaller sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multi-issue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections. (shrink)

This paper examines how the law elects non-Muslim leaders from the Qur’an perspective. The issue raised was based on the Regional Head Election of the DKI Jakarta on February 6, 2017 where one of the candidates is non-Muslim. Then, the simultaneous local elections on June 27, 2018, and the Legislative Election and the Presidential Election on April 17, 2019. It has become interesting because the issue of ethnic, racial, and religious sentiments in the context of candidate leaders often becomes a (...) serious consideration for voters, in addition to capability and track record of the candidate. This paper uses the thematic interpretation method seeks to get a comprehensive genealogy of the verse choosing non-Muslim leaders. The results studies that in the Qur'an there are four terms related to leadership: khalȋfah, uli al-amr, imâm, and awliyâ’. The last term gives rise to various interpretations because it is mentioned 33 times with various meanings: salvation, friend, and leader. From these verses it can be understood that partiality for non-Muslims is not permitted in Islam, especially in the affairs of the nashb al-Imâmah. As for the fulfillment of the rights of non-Muslims as citizens, it is still guaranteed and highly upheld in Islam. (shrink)

In this study, we propose a new direction of research on the axiomatic analysis of approval voting, which is a common democratic decision method. Its novelty is to examine an infinite population setting, which includes an application to intergenerational problems. In particular, we assume that the set of the population is countably infinite. We provide several extensions of the method of approval voting for this setting. As our main result, axiomatic characterizations of the extensions are offered by revealing (...) a direct link between approval voting and the Borda rule. The characterized methods are natural extensions of the standard approval voting method for the finite-population case and are regarded as minimum requirements for other possible infinite-population extensions, which are reasonably democratic. (shrink)

Panels, boards, and committees throughout society evaluate all manner of things by grading them, first individually and then collectively. Thus risks are prioritized, research proposals are funded, and candidates are shortlisted for jobs. It is not usual to pick winners in political elections by grading the candidates, but there are examples in history. This article takes up a question about the quality of judgments and decisions made by grading: under which conditions are they likely to be right? An answer comes (...) in the form of a jury theorem for median grading. Here, the collective grade for a thing is the median of its individually assigned grades—the one in the middle, when all of them are listed from "top" to "bottom." A second objective of this article is to suggest a solution to problems of voter ignorance in democracies. The idea is for democratic assemblies to use voting methods that make more of people's limited knowledge than do commonly used methods, such as majority voting. It turns out that in theory anyway, and perhaps also in practice, median grading can enable unenlightened assemblies to “track the truth”—even as majority voting would run them off the rails. (shrink)

In the context of computational social choice, we study voting methods that assign a set of winners to each profile of voter preferences. A voting method satisfies the property of positive involvement (PI) if for any election in which a candidate x would be among the winners, adding another voter to the election who ranks x first does not cause x to lose. Surprisingly, a number of standard voting methods violate this natural property. In this (...) paper, we investigate different ways of measuring the extent to which a voting method violates PI, using computer simulations. We consider the probability (under different probability models for preferences) of PI violations in randomly drawn profiles vs. profile-coalition pairs (involving coalitions of different sizes). We argue that in order to choose between a voting method that satisfies PI and one that does not, we should consider the probability of PI violation conditional on the voting methods choosing different winners. We should also relativize the probability of PI violation to what we call voter potency, the probability that a voter causes a candidate to lose. Although absolute frequencies of PI violations may be low, after this conditioning and relativization, we see that under certain voting methods that violate PI, much of a voter's potency is turned against them - in particular, against their desire to see their favorite candidate elected. (shrink)

In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning to losing. In this note, we prove a new impossibility theorem concerning this axiom: there is no ordinal voting method satisfying positive involvement that also satisfies the Condorcet winner and loser criteria, resolvability, and a common invariance property for Condorcet (...) class='Hi'>methods, namely that the choice of winners depends only on the ordering of majority margins by size. (shrink)

May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives. In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any preferential (...) voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, agrees with Minimax voting in all three-alternative elections, except perhaps in some improbable knife-edged elections in which ties may arise and be broken in different ways. (shrink)

Previous work by Diffo Lambo and Moulen [Theory and Decision 53, 313–325 (2002)] and Felsenthal and Machover [The Measurement of Voting Power, Edward Elgar Publishing Limited (1998)], shows that all swap preserving measures of voting power are ordinally equivalent on any swap robust simple voting game. Swap preserving measures include the Banzhaf, the Shapley–Shubik and other commonly used measures of a priori voting power. In this paper, we completely characterize the achievable hierarchies for any such measure (...) on a swap robust simple voting game. Each possible hierarchy can be induced by a weighted voting game and we provide a constructive proof of this result. In particular, the strict hierarchy is always achievable as long as there are at least five players. (shrink)

Summarization of legal case judgement documents is a practical and challenging problem, for which many summarization algorithms of different varieties have been tried. In this work, rather than developing yet another summarization algorithm, we investigate if intelligently ensembling (combining) the outputs of multiple (base) summarization algorithms can lead to better summaries of legal case judgements than any of the base algorithms. Using two datasets of case judgement documents from the Indian Supreme Court, one with extractive gold standard summaries and the (...) other with abstractive gold standard summaries, we apply various ensembling techniques on summaries generated by a wide variety of summarization algorithms. The ensembling methods applied range from simple voting-based methods to ranking-based and graph-based ensembling methods. We show that many of our ensembling methods yield summaries that are better than the summaries produced by any of the individual base algorithms, in terms of ROUGE and METEOR scores. (shrink)

Many bodies around the world make their decisions through voting systems in which voters have several options and the collective result also has several options. Many of these voting systems are anonymous, i.e., all voters have an identical role in voting. Anonymous simple voting games, a binary vote for voters and a binary collective decision, can be represented by an easy weighted game, i.e., by means of a quota and an identical weight for the voters. Widely (...) used voting systems of this type are the majority and the unanimity decision rules. In this article, we analyze the case in which voters have two or more voting options and the collective result of the vote has also two or more options. We prove that anonymity implies being representable through a weighted game if and only if the voting options for voters are binary. As a consequence of this result, several significant enumerations are obtained. (shrink)

In representative democracies, referendum voting and parliamentary elections provide two fundamentally different methods for determining the majority opinion. We use three mathematical paradoxes – so-called majority voting paradoxes – to show that referendum voting can reverse the outcome of a parliamentary election, even if the same group of voters have expressed the same preferences on the issues considered in the referendums and the parliamentary election. This insight about the systemic contrarieties between referendum voting and parliamentary (...) elections sheds a new light on the debate about the supplementary value of referendums in representative democracies. Using this insight, we will suggest legal conditions for the implementation of referendums in representative democracies that can pre-empt the conflict between the two methods for determining the majority opinion. (shrink)

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to such a problem as the \textit{discursive dilemma}. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, we address the question of how (...) good the various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and a Bayesian analysis. They correspond to group-internal and group-external decision-making, respectively. We compare those methods in a probabilistic model, demonstrate the robustness of our results over various generalizations and discuss their applicability in different situations. The findings vindicate (i) that in judgment aggregation problems, reasons should carry higher weight than conclusions and (ii) that considering members of an advisory board to be highly competent is a better strategy than to underestimate their advice.". (shrink)

It is well-known that different social choice procedures often result in different choice sets. The article focuses on how often this is likely to happen in impartial cultures. The focus is on Borda count, plurality method, max-min method and Copeland's procedure. The probabilities of Condorcet violations of the Borda count and plurality method are also reported. Although blatantly false as a descriptive hypothesis, the impartial culture assumption can be given an interpretation which makes the results obtained in impartial cultures particularly (...) significant, viz. the probabilities of deviations in choice sets indicate how far apart are the intuitions underlying various choice procedures. -/- . (shrink)

Numerous countries are heading toward digital infrastructures. In particular this new technology promises to help support methods for elections. However, one should be careful that such an infrastructure does not hinder the voting and representation issues. On the contrary, it should support those issues and help citizens have a clearer picture of the underlying mechanisms. This paper deals with the limits of voting procedures as they are described in classical collective choice theory and reflects on ways to (...) aggregate electronic votes stemming from various individuals that would be at the same time democratic, decisive and rational which is not feasible when candidate rankings alone are taken into account. This paper shows how electronic voting procedures could improve the situation by introducing preference-based votes. (shrink)

In this study, we are concerned with how agents can best amalgamate their private information about a binary state of Nature. The agents are heterogeneous in their “ability”, the quality of their private information. The agents cannot directly communicate their private information but instead can only vote between the two states. We first describe possible methods of sequential majority voting, and then we analyze a particular one: the first n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-1$$\end{document} (...) jurors vote simultaneously and, in the case of a tie, the remaining juror has the casting vote. We prove that when n=3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=3$$\end{document}, the probability of a correct verdict is maximized when the agent of median ability has the casting vote. (shrink)

The paper reflects on the methods democratic systems use for arriving at decisions. The most popular ones are elections where the majority rules and deliberative democracy. I argue that both of these do not measure up to the demands of democracy. Whether we use voting with majority rule or deliberative methods, only a portion of the citizenry is allowed to rule itself; minorities are always excluded. Instead of voting with majority ruler or deliberative methods, I (...) suggest that we employ mediation to reach agreement in democratic publics. (shrink)

The paper reflects on the methods democratic systems use for arriving at decisions. The most popular ones are elections where the majority rules and deliberative democracy. I argue that both of these do not measure up to the demands of democracy. Whether we use voting with majority rule or deliberative methods, only a portion of the citizenry is allowed to rule itself; minorities are always excluded. Instead of voting with majority ruler or deliberative methods, I (...) suggest that we employ mediation to reach agreement in democratic publics. (shrink)

This article has two goals: 1° to illustrate certain methods which are completely new in their application and ; 2° to communicate and analyse the results obtained by these methods.The first part of this study concerns the application of a mathematical model to the nominal votes in the French-speaking electoral college for the European elections of June 1984. The statistical categories of the log linear model, logically translated, permit to isolate and to measure the effects of list, position, (...) and personality of each candidate.The second part of the article studies in more detail the results for the candidates Happart and Nols. This provides the occasion to introduce and to illustrate a method which permits the measurement of the nature of the performance of each candidate in terms of votes and percentages. The application of this method to the totality of French - and Flemish -speaking candidates, with an interpretation of the significance of themeasures, forms the last part of this study. (shrink)

This paper provides a philosophical critique of social choice theory insofar as it deals with the normative evaluation of voting and voting rules. I will argue that the very method of evaluating voting rules in terms of whether they satisfy various conditions is deeply problematic because introducing strategic behaviour leads to a violation of any condition that makes a difference between voting rules. I also argue that it is legitimate to make interpersonal comparisons of utilities in (...) voting theory. Combining a realistic account of voters’ behaviour with a utilitarian evaluation of the outcomes then leads to the judgment that strategic voting is beneficial. If it is, then Arrow's theorem does not have far-reaching consequences for democracy because one of its conditions is not normatively acceptable. (shrink)

A major problem for interpersonal aggregation is how to compare utility across individuals; a major problem for decision-making under normative uncertainty is the formally analogous problem of how to compare choice-worthiness across theories. We introduce and study a class of methods, which we call statistical normalization methods, for making interpersonal comparisons of utility and intertheoretic comparisons of choice-worthiness. We argue against the statistical normalization methods that have been proposed in the literature. We argue, instead, in favor of (...) normalization of variance: we claim that this is the account that most plausibly gives all individuals or theories ‘equal say’. To this end, we provide two proofs that variance normalization has desirable properties that all other normalization methods lack, though we also show how different assumptions could lead one to axiomatize alternative statistical normalization methods. (shrink)

We examine collective decision-making in a jury voting game under the unanimity rule when voters have ambiguous beliefs. Unlike in existing studies (Ellis in Theoretical Economics 11:865–895, 2016; Fabrizi et al., in: AUT Economics Working Paper, 2021; Ryan in Theory and Decision 90:543–577, 2021), the locus of ambiguity is the likelihood function (signal precision) rather than the prior. This significantly alters the properties of symmetric equilibria. While prior ambiguity may induce multiple equilibria (Fabrizi et al., in: AUT Economics Working (...) Paper, 2021; Ryan in Theory and Decision 90:543–577, 2021) we show that, under likelihood ambiguity, there exists a unique non-trivial symmetric responsive equilibrium that takes the same form as in the absence of ambiguity (Feddersen and Pesendorfer in The American Political Science Review 92:23–35, 1998). Moreover, likelihood ambiguity partially offsets the pernicious effects of pivotality on decision quality: the frequency of Type I error (convicting the innocent) is typically lower than in the absence of ambiguity. (shrink)

In this paper, we offer the spanish translation with notes of three treatises of Ramon Llull : Artificium electionis personarum, the chapter XXIV of book II from Llibre d’Evast, d’Aloma e de Blaquerna named «En qual manera Natana fo eleta a abadessa» and De arte electionis. These three texts show a new election technique supported on the Ars magna methods. The translations are preceded by a short introduction explaining the place that such texts occupy in the whole lullian opus (...) and the advances of recents investigations. (shrink)

Designing a mechanism that provides a direct incentive for an individual to report her utility function over several alternatives is a difficult task. A framework for such mechanism design is the following: an individual (a decision maker) is faced with an optimization problem (e.g., maximization of expected utility), and a mechanism designer observes the decision maker’s action. The mechanism does reveal the individual’s utility truthfully if the mechanism designer, having observed the decision maker’s action, infers the decision maker’s utilities over (...) several alternatives. This paper studies an example of such a mechanism and discusses its application to the problem of optimal social choice. Under certain simplifying assumptions about individuals’ utility functions and about how voters choose their voting strategies, this mechanism selects the alternative that maximizes Harsanyi’s social utility function and is Pareto-efficient. (shrink)

While simulation has been a staple of Social Studies curricula since the 1960s, few current studies have sought to understand the mechanisms behind how simulations may influence students’ learning and behavior. Learning theories around student engagement – specifically interest development theory (Hidi & Renninger, 2006) – may help explain students’ commitment to future political action. To incorporate this theory into the democratic education literature, this study asks: Do situational interest and simulation frequency uniquely contribute to students’ commitment to vote in (...) the future? Data included 260 students from 19 classrooms, 9 teachers, in 9 schools, recruited as part of a larger mixed-methods study on Project Based Learning. Hierarchical Linear Modeling (HLM) techniques were used to examine the relationship between individual outcomes and predictors across different classrooms and teachers. Analysis of data suggests both frequency of simulations and situational interest directly predict students’ commitment to vote but do not uniquely contribute to the outcome. Findings suggest situational interest may play an important role in influencing students’ learning and future political behavior. (shrink)

Summary In this article, using archival sources we show how mathematical knowledge and methods helped to solve the problem of the election of the first exclusively Bulgarian government in the peaceful election in 1879 and 1880. We will describe the situation in Bulgaria, and especially the role of the mathematician, politician and financier Ivan Petrov Salabashev (1853–1924).

Delaware case law has rendered the tender offer obsolete as a method for purchasing a company whose directors oppose the acquisition. A potential acquirer facing target opposition today must run an insurgent director slate, in the expectation that its directors are more likely to sell. The Delaware courts have not justified their preference for elections over markets as the preferred vehicle for implementing changes in control. Informal scholarly analyses ask transaction cost questions, such as whether proxy contests are more costly (...) than takeovers. This article attempts to break new ground by asking whether there are systematic differences in the performance of elections and markets in the corporate context. Recent models of voting processes, we argue, strongly suggest that elections are inferior to markets. Proxy contest elections sometimes can be won by incumbent managements when a transfer of control would be efficient, a conclusion consistent with the sparse data; and the proxy election process aggregates information regarding the sale decision less well than markets do, thereby implying that proxy voters are less well-informed. Theory and data thus suggest, at the least, that the intellectual burden of proof should change: the task now is to justify using elections to transfer control despite their apparent deficiencies. The article briefly considers the policy implications of this change in perspective. (shrink)

In comparative electora/ studies, the Belgian electoral formula is classified in different, sometimes rather conflicting, classes. This paper is primarily concerned with the question if the Belgian electoral system truely is a D'Hondt system? In the first part I argued that the D'Hondt method, as a divisor sequence, can be applied alternatively. This modified method departs from a Hare-quota in the first phase. To allocate the rest seats in the second phase, the parties' aggregated vote totals are divided by the (...) number of seats obtained in phase one, added by 1, then 2, then 3 etc. Like all divisor methods, the highest averages are used to assign the rest seats. This alternative D'Hondt method produces exactly the same resu!ts as the classical method D'Hondt. Thus, it is also used in the Belgian two-tier-districting system. Furthermore, the Belgian electoral system can be classified as a proper D'Hondt system while ignoring the primary districts. (shrink)

By classic results in social choice theory, any reasonable preferential voting method sometimes gives individuals an incentive to report an insincere preference. The extent to which different voting methods are more or less resistant to such strategic manipulation has become a key consideration for comparing voting methods. Here we measure resistance to manipulation by whether neural networks of varying sizes can learn to profitably manipulate a given voting method in expectation, given different types of (...) limited information about how other voters will vote. We trained over 70,000 neural networks of 26 sizes to manipulate against 8 different voting methods, under 6 types of limited information, in committee-sized elections with 5-21 voters and 3-6 candidates. We find that some voting methods, such as Borda, are highly manipulable by networks with limited information, while others, such as Instant Runoff, are not, despite being quite profitably manipulated by an ideal manipulator with full information. For the two probability models for elections that we use, the overall least manipulable of the 8 methods we study are Condorcet methods, namely Minimax and Split Cycle. (shrink)

Recent research has shown that in referendum elections, the presence of interdependence within voter preferences can lead to election outcomes that are undesirable and even paradoxical. However, most of the examples leading to these undesirable outcomes involve contrived voting situations that would be unlikely to occur in actual elections. In this paper, we use computer simulations to investigate the desirability of referendum election outcomes. We show that highly undesirable election outcomes occur not only in contrived examples, but also in (...) randomly generated elections. Our data suggest that the presence of interdependent preferences significantly increases the likelihood of such undesirable outcomes, and that certain alternative voting methods, such as sequential voting and setwise aggregation, hold the potential to produce outcomes that more accurately reflect the will of the electorate. (shrink)

In ‘Normative Uncertainty as a Voting Problem’, William MacAskill argues that positive credence in ordinal-structured or intertheoretically incomparable normative theories does not prevent an agent from rationally accounting for her normative uncertainties in practical deliberation. Rather, such an agent can aggregate the theories in which she has positive credence by methods borrowed from voting theory—specifically, MacAskill suggests, by a kind of weighted Borda count. The appeal to voting methods opens up a promising new avenue for (...) theories of rational choice under normative uncertainty. The Borda rule, however, is open to at least two serious objections. First, it seems implicitly to ‘cardinalize’ ordinal theories, and so does not fully face up to the problem of merely ordinal theories. Second, the Borda rule faces a problem of option individuation. MacAskill attempts to solve this problem by invoking a measure on the set of practical options. But it is unclear that there is any natural way of defining such a measure that will not make the output of the Borda rule implausibly sensitive to irrelevant empirical features of decision-situations. After developing these objections, I suggest an alternative: the McKelvey uncovered set, a Condorcet method that selects all and only the maximal options under a strong pairwise defeat relation. This decision rule has several advantages over Borda and mostly avoids the force of MacAskill’s objection to Condorcet methods in general. (shrink)

The technical changes in the local-elections law that were recently implemented have only had a negligible effect on the electoral results. As a matter of fact they did not bring about any change in the two major evils that beset local elections in Belgium. These are indeed dominated by a particular system of allocation of seats that systematically deviates from proportional representation and is heavily resented as such by a considerable part of the public opinion. The recent modifications allow a (...) voting method that wilt - from now on and increasingly so in the future - give a possibility to particular factions that are slightly stronger within a certain party to conquer a far more than proportional share of the party seats andmight well come close to the total number of seats allocated to a certain party. It is indeed the democratic nature of the electoral system in Belgium that is at stake here. (shrink)

Collective rationality has attracted much attention by formal theorists, but philosophically, much of it is still poorly understood. The difficulties are easily motivated. As long as we only aggregate preferences (as we do in the case of majoritarian decision-making), there are different proposals for how to do so, and arguments on their behalves can be developed. However, there are voting methods that use rankings other than ordinal ones, and arguments for specific preference-based methods fail to be effective (...) against such methods. For example, no such argument can address a proposal that, say, a committee should make a hiring decision by using a 100-point system. On this proposal, each committee member assigns between 0 and 100 points to each applicant, and then these assignments are aggregated by, for example, averaging. Would that system be as reasonable as purely preference-based methods? Or can we distinguish conditions under which ordinal rankings are appropriate from conditions under which other rankings are appropriate? Such questions call for a theory of voting methods that assesses, first, the conditions under which particular kinds of rankings are appropriate (e.g., ordinal or point systems); second, what specific voting method(s) is (are) appropriate for the specific kinds of rankings; and third, what the criteria for appropriateness are in both cases. Recall that I explained at the start that my most of my research could be understood as interrogating notions of justice and fairness: it is through this search for criteria of appropriateness that considerations of fairness enter here. We are far from having such a theory, and it is precisely this point that keeps me fascinated with this area. (shrink)

To explore the change of brain connectivity in schizophrenics, the resting-state EEG source functional connections of SCZ and healthy control were investigated in this paper. Different band single-layer networks, multilayer networks, and improved multilayer networks were constructed and their topological attributes were extracted. The topological attributes of SCZ and HC were automatically distinguished using ensemble learning methods called Ensemble Learning based on Trees and Soft voting method, and the effectiveness of different network construction methods was compared based (...) on the classification accuracy. The results showed that the classification accuracy was 89.38% for α band network, 82.5% for multilayer network, and 86.88% for improved multilayer network. Comparing patients with SCZ to those with Alzheimer’s disease, the classification accuracy of improved multilayer network was the highest, which was 88.12%. The power spectrum in the α band of SCZ was significantly lower than HC, whereas there was no significant difference between SCZ and AD. This indicated that the improved multilayer network can effectively distinguish SCZ and other groups not only when their power spectrum was significantly different. The results also suggested that the improved multilayer topological attributes were regarded as biological markers in the clinical diagnosis of patients with schizophrenia and even other mental disorders. (shrink)

Many voting rules and, in particular, the plurality rule and Condorcet-consistent voting rules satisfy the simple-majority decisiveness property. The problem implied by such decisiveness, namely, the universal disregard of the preferences of the minority, can be ameliorated by applying unbiased scoring rules such as the classical Borda rule, but such amelioration has a price; it implies erosion in the implementation of the widely accepted majority principle . Furthermore, the problems of majority decisiveness and of the erosion in the (...) majority principle are not necessarily severe when one takes into account the likelihood of their occurrence. This paper focuses on the evaluation of the severity of the two problems, comparing simple-majoritarian voting rules that allow the decisiveness of the smallest majority larger than 1/2 and the classical Borda method of counts. Our analysis culminates in the derivation of the conditions that determine, in terms of the number of alternatives k, the number of voters n, and the relative (subjective) weight assigned to the severity of the two problems, which of these rules is superior in light of the dual majoritarian approach. (shrink)